The R9 290 and R9 290x would be bottlenecked. The R9 280x maybe a little, but the R9 280 and R9 285 should be fine with the FX-6300. Overclock will help but its not necessary.
If you feel like its starting to have bad issues go buy an FX 8320 or FX 8320E. Make sure it works with your motherboard first, but I still doubt you will have too much issue. Another user had a Phenom II x4 at 3.33Ghz and a Nvidia GTX 760 the other day, the GTX 760 is close to an R9 280, and the Phenom II x4 is quite a bit slower than the FX 6300. He had bottleneck, but it wasn't extreme. Based off that you should be fine.